When individuals face rationing on a particular market, they will seek to amend their trade offer on this and other markets to account for the extra constraint on their behaviour. Empirical researchers must attempt to mimic this behaviour by specifying effective demand functions. There is no consensus, however, about how this should be done. The development of applied multi-market disequilibrium modelling has given this problem an immediate practical relevance. Moreover, aggregation and computational considerations further complicate the problem of specifying theoretically consistent yet tractable effective demands. This paper explores theoretical aspects of empirical effective demand functions and in this light reviews the existing empirical literature. We stress the practical nature of the problems encountered in applied work and the limited guidance that theory provides. The initial systematic discussion of the problems involved in specifying empirical effective demand functions in Portes (1977) has been supplemented by Gourieroux, Laffont and Monfort (1980), Ito (1980), Sneessens (1981) and Lee (1986). Our paper is partly an update of this work. There are three main candidates differing according to both the measurement of excess demand on other markets and how individuals are assumed to respond to this. Using linear forms for the effective demands, Portes showed how the three candidates are observationally equivalent, in that they all imply the same level of trade. Perhaps because of this, we find a wide range of effective demand concepts used in existing empirical applications. We then consider the implications for empirical effective demand functions of allowing rationing to operate at a disaggregated level. These "smoothing-by-aggregation" models have been the most significant